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Question: If different words are found from letters of the word "UNIVERSITY", then the probaility that two I'...

If different words are found from letters of the word

"UNIVERSITY", then the probaility that two I's do not come

together

A

45\frac { 4 } { 5 }

B

65\frac { 6 } { 5 }

C

25\frac { 2 } { 5 }

D

35\frac { 3 } { 5 }

Answer

45\frac { 4 } { 5 }

Explanation

Solution

Total words = II, U,N,V,E,R,S,T,Y = 10!2!\frac { 10 ! } { 2 ! } fav. words

= 8 ! × 9C2 × 2!2!\frac { 2 ! } { 2 ! }

\ Prob. = 9×810×9\frac { 9 \times 8 } { 10 \times 9 } = 45\frac { 4 } { 5 }